虚谱法波动方程深度偏移

对二维标量波动方程进行 Claerbout 坐标变换,再变换到频率-空间域,可得到隐含关于 x 的高阶偏导数的高阶近似方程。通过正、反两次 Fourier 变换即虚谱法可求得关于 x 的高阶偏导数项,最终实现地震资料的波动方程深度偏移。文中还描述了延拓算子的设计及延拓步长的选择,最后通过理论模型验证了该方法是正确和可行的。

Pscudospectral wave equation depth migration

If we first make Claerbout}s coordinate transformation of a 2D scalar wave equation and then transform the equation into frequencyspace domain, we can obtain the higher -order approximate equation which implicitly consists of higher partial derivatives with respect to x, The perform of forward and inverse Fourier transforms, namely,the pseudospectral method, brings us higher partial derivatives with respect to x; then the final wave equation depth migration can be achieved, It is described how we design continuation operator and choose continuation steps, Theoretical model proves this method right and feasible.